KABUL, Afghanistan (CNN) -- Afghan President Hamid Karzai said Wednesday that his first demand of the new U.S. administration will be "no civilian casualties in Afghanistan."

Karzai made an appeal to U.S. election winner Obama.

He spoke as the U.S. military in Afghanistan announced a joint investigation with the Afghan government into reports that a U.S. airstrike this week killed 35 civilians, including women and children.

"We cannot win the fight against terrorism with airstrikes and battles in Afghanistan's villages," Karzai said. "This is our first and main demand, to stop civilian casualties."

The airstrike happened Monday in the Shah Wali Kot district of Afghanistan's southern Kandahar province, the military said in a news release. A Taliban spokesman said the "enemy" airstrikes killed 35 civilians, including women and children who may have been part of a wedding party.

Karzai spoke during a news conference in which he congratulated Barack Obama for winning the U.S. presidential race, but stressed that "the civilian casualties should be stopped in Afghanistan."

The outcry over the civilian deaths comes during the first visit to Afghanistan by Gen. David Petraeus as the top U.S. military commander in the region.

Petraeus, who took over as head of U.S. Central Command on October 31, met Wednesday with Afghan Defense Minister Abdul Rahim Wardak.

He is scheduled to meet other Afghan, U.S., and NATO military leaders during his visit as well.

The U.S. military said it would investigate the reported civilian deaths in Shah Wali Kot along with Afghanistan's Interior Ministry.

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"Though facts are unclear at this point, we take very seriously our responsibility to protect the people of Afghanistan and to avoid circumstances where non-combatant civilians are placed at risk," said U.S. Forces Afghanistan spokesman Cmdr. Jeff Bender.

"If innocent people were killed in this operation, we apologize and express our condolences to the families and the people of Afghanistan."

Taliban spokesman Qari Mohammad Yousif Ahmadi said its forces, from Monday until early Wednesday, had engaged in a firefight with "enemy forces" in which 13 soldiers and one Taliban fighter were killed.

During the firefight, airstrikes were called in, leading to the 35 civilian deaths and injury of a further 15, he said.

Wali Karzai, the head of the Kandahar provincial council and Karzai's brother, confirmed that "some civilians were killed and wounded in an airstrike by foreign forces in Shah Wali Kot district, but we don't know how many."

He said the aerial bombardment was conducted after Afghan and foreign forces were attacked by militants in the area.

Relations between the United States and Afghanistan were rankled when a U.S. airstrike in late August killed dozens of civilians in the Shindand District of the western Afghan province of Herat.

Afghan and United Nations officials said 90 civilians, mostly women and children, were killed in the August 22 strike. The U.S. military initially denied any civilians were killed. But when cell phone pictures were later provided to the U.S. military showing dozens of bodies at the scene of the strike, the top U.S. military commander in Afghanistan, Gen. David McKiernan, asked U.S. Central Command to review the initial investigation.

That investigation conceded that 33 civilians were killed.

Weeks after the deadly strike, U.S. Secretary of Defense Robert Gates traveled to Kabul, where he met with Karzai and publicly apologized for the incident.